But even if Ajax was able to limit traffic sent from the server and get rid of manual page reloads it still had no way of knowing whether the server had any new data to be downloaded unless it kept requesting the server in regular intervals.

Does that mean, like:

Yo, can I have that server, in Major Seconds, please?
Yo, can I have that server, in Minor Thirds, please?
Yo, can I have that server, in Fifths, please?
Yo, can I have that server, in an Octave, please?

I assume it is not clear to you how the server can send data to the client without a page refresh, right?

Meteor uses websockets as a permanent connection between the client and the server. So there is no 'polling' from the client every X seconds.

Meteor follows the publication and subscribe methodology. That means:

ClientA: Hey Server, I want to know if there are any new movies! [Subscribe]
Server receives a new movie.
Server checks who wanted to know if there are new movies
Server: Hey ClientA, here is a new movie, its name is "Back to the future 4". [Publish]